Non-contact force microscope having a coaxial cantilever-tip configuration

ABSTRACT

The present invention comprises a highly sensitive non-contact force microscope having a coaxial cantilever-tip configuration and a method of forming such configuration. The non-contact microscope obtains high resolution graphical images of a sample surface topography, and/or other properties thereof including its electrostatic, magnetic, or Van der Waals forces.

Some of the work resulting in this invention was performed under Officeof Naval Research Grant No. N 00014-88-K-0094 and the United States mayhave certain rights to this invention.

This application is a divisional of pending U.S. patent application Ser.No. 08/241,745 filed on May 12, 1994 for NON-CONTACT FORCE MICROSCOPEHAVING A COAXIAL CANTILEVER-TIP CONFIGURATION, now U.S. Pat. No.5,509,300.

INTRODUCTION

This invention relates generally to the field of force microscopy andmore particularly to a novel and unique force microscope having acoaxial cantilever-tip configuration for ultra sensitive non-contactdetection of forces and force gradients. This configuration, with thecantilever and tip having a substantially common axis, facilitates thepractice of non-contact force microscopy, such as in the measurement oflong-ranged electrostatic interactions, Van Der Waals forces, magneticforces, and the like.

BACKGROUND OF THE INVENTION

Scanning probe microscopy refers generally to a class of high resolutiontechniques for studying surfaces at or near atomic resolution. Severaldifferent techniques which produce these results have been described inthe prior art.

One of the first such techniques is scanning tunneling microscopy (STM),which utilizes a sharpened tip held in electrical contact (circa 0.1 to1 nm) with a sample surface, and biased to produce a current between thetip and the surface. Current variations caused by differences in thedistance between the tip and the surface may be plotted to yield atopographical representation of the surface. This technique is describedin Binnig et al. (U.S. Pat. No. 4,343,993). In Binnig, the tip and thesample must be electrically conductive to allow current flow betweenthem, and as such, limits the application of this technique. Anotherlimitation is that the STM is sensitive only to the charge density atthe surface of the sample.

A later variant of scanning probe microscopy was described by Binnig,Quate, and Gerber who reported the earliest atomic force microscope(AFM). (See: Binnig et al., Physics Review Letters, Vol. 56, page 930(1986)). This early atomic force microscope, as further described inBinnig (U.S. Pat. No. 4,724,318), utilizes a small, diamond microprobetip mounted on the side of a soft cantilever, so that the axes of thecantilever and the tip are substantially perpendicular to one another.The tip is brought into close proximity (0.1 to 1 nm) to the sample,with the cantilever disposed parallel to the sample, so that therepulsive forces between the tip and surface cause deflections of thecantilever.

In the Binnig AFM application, the tip is attached to a conductivecantilever which is interposed between the sample surface and a standardSTM tip. A tunneling current is then maintained between the AFMcantilever and the STM tip, so that the sample need not be conductive.Changes in the current flow between these two elements provide asensitive measure of the deflections of the AFM cantilever, and hence ofthe forces between the sample surface and the tip. More recent and morecommon AFM applications use other techniques, such as optical methods,to measure cantilever deflection.

In one mode of operation, changes in the deflection of the cantileverare measured as the tip is rastered over a sample. In practice, the tipscans the sample in very close proximity (<1 nm) to the sample surface,so that the deflections of the cantilever are due to the repulsiveforces between the atoms on the sample and the atoms on the apex of thetip.

As was immediately recognized by Binnig et al., a generally superiormode of operation utilizes dynamical techniques to reduce noise, andthereby increase sensitivity. By vibrating the cantilever perpendicularto the plane of the sample (i.e. vertically relative to a horizontallydisposed sample) at the mechanical resonance frequency of thecantilever, noise is reduced by the quality factor of the mechanicalresonator and by the narrow frequency range of the measurement. Apossible disadvantage of this "resonance enhancement" configuration isthat it is sensitive primarily to force gradients in the direction ofvibration, the net force perpendicular to the sample surface(Z-direction) must still be determined from the static deflections ofthe cantilever.

Furthermore, a fundamental drawback of the Binnig AFM geometry is thatthe tip can only be vibrated in a direction that is substantiallyperpendicular/to the sample surface. Thus, although forces between thetip and sample act in all directions of XYZ space, only the forcegradients in the direction of oscillation (Z-direction) can be sensed bya cantilever that is oriented parallel to the sample surface; importantinformation about the forces in the X- and Y-directions cannot beresolved.

Mate et al. (Phys. Rev. Lett., 59 pg. 1942 (1987)) describe a frictionalforce microscope for measuring lateral forces (see also Meyer and Amer,Appl. Phys. Lett., vol. 57 pg. 2089 (1990) and Marti et al.,Nanotechnology, vol. 1 pg. 141 (1990)). The cantilever-tip configurationof these frictional force microscopes is similar to that of the BinnigAFM (with the cantilever axis oriented substantially parallel to thesample's surface), but lateral forces are measured from the torsionalrotation of the cantilever about its axis. This configuration, however,has some fundamental drawbacks that limits its sensitivity to lateralforces. First, the cantilever spring constant is always stiffer againsttorsional rotation than it is against normal displacement. Second, it isgenerally difficult to excite torsional modes of vibration, hence noresonant enhancement of the lateral force resolution has been achievedwith these microscopes. Finally, only forces in one lateral direction(for example, in the X-direction, but not the Y-direction) can bemeasured at a time.

Taubenblatt (Appl. Phys. Lett., vol. 54 page 801 (1989)) describes adifferent configuration for atomic force microscopy. The Taubenblattmicroscope utilizes a vertically mounted STM tip, which can be made tovibrate laterally over the surface of a horizontally disposed sample.Changes in the vibrational frequency of the STM tip provide informationabout changes in the lateral atomic forces between the tip and thesample, thus rendering simultaneous STM and AFM images. The TaubenblattSTM/AFM microscope requires that the tip and sample be made fromelectrically conductive materials. Furthermore, the tip and sample mustcarry a possibly damaging electrical current. Finally, during imaging,the tip must be kept in close proximity to the sample surface, so itcannot be used for non-contact force microscopy.

Pohl (U.S. Pat. No. 4,851,671) describes a similar configuration for themeasurement of lateral atomic forces. The Pohl AFM utilizes a rigidmicroprobe tip attached to (or etched from) a quartz crystal oscillator.In practice, the tip is brought into close proximity to the sample (<1nm), and the tip is vibrated laterally across the sample surface.Changes in the resonance frequency of the quartz crystal provideinformation about the force gradients at the surface in the direction ofoscillation.

A fundamental drawback of the Pohl AFM is that the oscillator consistsof a quartz crystal, which has a static spring constant of approximately4×10⁶ N/m. Generally, such a "stiff" spring constant AFM requirescomplex instrumentation to achieve the sensitivity of a typical "soft"cantilever (0.01-100 N/m) AFM. Specifically, Pohl uses a sophisticatedfrequency counter, capable of resolving changes of 2 parts per billionin the frequency of the crystal, for sensitivity (2×10⁻¹² N) comparableto that of a simple "soft" cantilever AFM. Furthermore, such frequencyresolution requires relatively long integration times (about 1 secondper point), which limits the scan speed to several minutes per line.Finally, because of the very high spring constant of the quartz crystaloscillator, the Pohl microscope does not interact detectably with thesample until the tip is in close proximity (within 0.1 to 1 nm) of thesample surface, thus the Pohl microscope is limited to the measurementof relatively strong interatomic forces.

Sometimes it is desirable to measure other types of forces from asample. Abraham (U.S. Pat. No. 4,992,659) teaches an electro-magneticforce microscopy means and method whereby Lorentz forces arising fromthe interaction of a current interposed between the metallic conductivetip and a conductive sample surface are measured. Lorentz forces arethose forces that arise when the current flow between the tip and sampleof a STM system are deflected by a magnetic field.

Abraham's preferred tip is non-magnetic to eliminate extraneous forcescreated by a magnetic tip. When an STM current is interposed between theconductive tip and the conductive sample, Lorentz force(electro-magnetic) induced deflections of the vibrating tip can bemeasured. The strength of the force, and hence the magnitude of thedeflection, is plotted using laser positioning instrumentation.Fundamental limitations of the Abraham Lorentz force microscope includethat the sample must be conductive, and that a potentially damaging andinvasive current must pass through the surface.

Furthermore, as in the other prior art techniques for contact AFMsdescribed above, the Abraham microprobe tip must be placed at a distanceof approximately 1 nm (or less) from the surface to be studied. Toobtain a complete image, this close proximity must be maintainedthroughout the scan. Thus, to follow the contours of a sample, rapidmotion of the tip assembly must be made to avoid catastrophicimpingements (crashes) of the tip onto the sample. This indicates thatonly microscopically smooth regions of a surface may be investigatedsuccessfully, which is an obvious deficiency when the investigatordesires to study an irregular surface.

Some improvements in the prior art have been made by operating standard(perpendicular cantilever-tip configuration) AFMs in non-contact mode.In non-contact mode, the AFM tip is held farther from the sample (1-100nm), where a diversity of longer-ranged interactions such as magnetic,Van der Waals, or electrostatic dipole forces may be resolved. Ingeneral, these long-ranged forces are weaker and more dispersed than theinter-atomic forces measured by contact AFM, which thus has theadvantage of diminishing the possibly destructive forces that the tipimparts on the sample, but demands that maximum sensitivity be availablefor near atomic resolution.

Any force microscope that incorporates a tunneling current between thesample and tip (such as the Taubenblatt AFM/STM or the Abrahamnear-field Lorentz magnetic force microscope) cannot be operated innon-contact mode. Moreover, any force microscope with limited forceresolution (such as the Pohl oscillating quartz AFM) cannot be operatedin non-contact mode. All prior art AFMs that have been operated innon-contact mode have embodied the original Binnig configuration of atip that is substantially perpendicular to the cantilever, but thisconfiguration has some fundamental drawbacks. First, the tip can only bevibrated in a direction substantially perpendicular to the surface ofthe sample, hence the primary contrast mechanism is due only to forcegradients in the Z-direction. Second, information about the X- andY-forces along the surface of the sample can only be obtained by usingless sensitive torsional force sensing. Third, large variations in theforce between the surface and the tip often cause uncontrolleddeflections of the cantilever toward the sample surface, resulting incatastrophic tip-to-sample collisions (tip crashes). To reduce theincidence of tip crashes, cantilevers that are relatively rigid must beused, which limits the ultimate sensitivity of all force microscopesthat are based on the original Binnig AFM configuration.

Although the prior art has addressed certain limitations in the art ofscanning probe microscopy, none overcome all of the disadvantages.Accordingly, the present invention is directed toward providing to theart of force microscopy a novel means of producing high resolutionanalysis of a surface, either conductive or non-conductive, at a tipdistance which will not contact (through electric current orinadvertence) the surface under study. A further goal is to provide atip configuration which allows for measurement of both axial andmulti-directional lateral forces, is effective in ambient conditions, issensitive to small force gradients, and can be obtained usinginexpensive laboratory instrumentation.

BRIEF SUMMARY OF THE INVENTION

The present invention provides a new and highly sensitive non-contactforce microscope which overcomes substantially all of the deficienciesfound in the prior art. More particularly, the present inventionprovides a new, highly sensitive and versatile configuration for thecantilever and microprobe tip in such a microscope. The novelconfiguration has a sharpened tip that is attached to (or formed from)the end of a cantilever, so that the cantilever and tip havesubstantially a common axis, and this common axis is orientedsubstantially perpendicular to the surface of the sample to be imaged.Thus, the geometry may be described as a coaxial cantilever-tipconfiguration, which when mounted vertically over the surface of ahorizontally disposed sample, is made to vibrate horizontally(laterally) over the surface, somewhat like a tiny pendulum. Further,the tip is disposed at non-contact distances (that is greater than 1 nm)from the sample, and is most useful in measuring forces other than therepulsive atomic forces which dominate at distances of less than 1 nmfrom the sample. Furthermore, when the tip is magnetized, the structureof the present invention may be adapted for magnetic force microscopy,as described by DiCarlo et al., Applied Physics Letters, vol. 61 pg.2108 (1992).

The coaxial cantilever-tip configuration of the present invention hasseveral fundamental advantages over prior art force microscope designs.

First, the microscope embodying the present invention is especially andunexpectedly useful as a non-contact force microscope, where the tip isheld at relatively large distances (1-100 nm) from the sample surface.As will be shown, non-contact force microscopy has some fundamentaladvantages over prior techniques, which were limited to imaging therepulsive forces between overlapping atoms. At sample-to-tip distancesof greater than 1 nm, other, often more interesting interactions such asmagnetic, Van der Waals, or electrostatic forces may be imaged. Suchlong-ranged and dispersed interactions reduce the possibly damaginginfluence of the tip on the sample, and similarly reduce the need tohave a microscopically clean surface.

Second, the coaxial cantilever-tip configuration is intrinsicallysimpler and ultimately more sensitive than prior designs. Usinginexpensive laboratory instrumentation, a simple non-contact magneticforce microscope that gives state-of-the-art sensitivity has beenobtained.

Third, similar to the fact that the period of a pendulum depends on theforce of gravity, the vibration frequency of the coaxial cantilever-tipconfiguration depends on the normal (Z-component) force out of a sample.This advantage is primarily useful for characterizing large homogeneousregions of a sample, since the contrast mechanisms of microscopicstructures are usually dominated by force gradients which are measurablewith this configuration.

Fourth, since the tip is oscillated laterally with respect to thesample's surface, the primary contrast mechanism is due to changes thatoccur laterally across the sample. Often it is these lateral changesthat are of primary interest. For example, in standard magneticrecording technology, the recorded signal consists of lateral changes inthe magnetization across the magnetic recording media. The coaxialcantilever-tip configuration provides the most direct microscopicmeasurement available of such recorded signals.

Fifth, the tip may be oscillated in the X- or Y-directions, providinginformation about the magnitude and direction of the lateral forces atthe surface of a sample, with a single, highly sensitive forcecantilever. In fact, by adding a second deflection detector, it would bepossible to simultaneously obtain the force gradients in both the X- andY-directions.

Lastly, the coaxial cantilever-tip configuration described herein, whichis oriented substantially perpendicular to a sample's surface, prohibitsdeflections towards the surface, thereby reducing the incidence of tipcrashes and permitting the use of ultra-small spring constantcantilevers for superior force sensitivity. It is true that forsufficiently strong lateral forces, a soft cantilever may beirreversibly displaced along the sample's surface; but since thesedeflections do not result in a potentially damaging tip crash, they donot seriously affect the imaging process. Furthermore, for the coaxialcantilever-tip configuration, the primary microscopic contrast mechanismis provided by these same lateral forces, thus a stiffer cantilever canbe used without sacrificing image contrast.

It is therefore the principal object of the present invention to providea novel and unique non-contact force microscope, having a coaxialcantilever-tip configuration, which is highly sensitive to both thenormal forces from a sample and multi-directional lateral forcegradients, thereby providing high resolution topographical data, orother force data such as magnetic or electric field measurements, fromthe sample under study.

It is a further object of the present invention to provide a coaxialcantilever-tip configuration for a non-contact force microscope whoseoscillations may be measured in any lateral direction across a sample'ssurface, thereby yielding valuable directional information about theforces.

Another object of the present invention is to provide a coaxialcantilever-tip configuration for a non-contact force microscope whichhas a low static spring constant to efficiently yield increasedmeasurement precision, and which is particularly sensitive to smallforce gradients.

A still further object of the present invention is to provide a coaxialcantilever-tip configuration for a non-contact force microscope which isrelatively stiff perpendicularly relative to the sample, to preventsurface collisions (tip crashes), and yet remain highly sensitive to thelateral force gradients.

Still another object of the present invention is to provide a forcemicroscope which operates at non-contact distances, minimizestip-to-sample invasiveness, is effective with conductive andnonconductive sample materials, and which is particularly useful formeasuring lateral force gradients.

Yet another object of the present invention is to provide a non-contactforce microscope which is operational under normal atmospheric andtemperature conditions.

These and still further objects, as shall hereinafter appear, arereadily fulfilled by the present invention in a remarkably unexpectedmanner as will be readily discerned from the following detaileddescription of an exemplary embodiment thereof, especially when read inconjunction with the accompanying drawings in which like numbers bearlike indicia throughout the several views.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a vertical cross sectional view of a force microscope, incombination with a coaxial cantilever-tip configuration, embodying thepresent invention;

FIG. 2 is a perspective view of a coaxial cantilever-tip configurationand capacitance probe embodying the present invention;

FIG. 3(a) is a magnetic force image of a recorded region of VHS videotape;

FIG. 3(b) shows the measured magnetic contrast profile along a line ofimage 3(a);

FIG. 3(c) shows the calculated magnetic contrast profile for theconditions of FIG. 3(b);

FIG. 4(a) shows a magnetic force image of a recorded region of VHS videotape, obtained with the microprobe tip vibrated in a directionperpendicular to the magnetic transitions;

FIG. 4(b) shows a magnetic force image of a recorded region of VHS videotape, with the microprobe tip vibrated in a direction parallel to themagnetic transitions;

FIG. 5 shows a large area magnetic force image of the superposed audioand video signals on a region of s-VHS video tape.

FIG. 6 shows a high resolution magnetic force image of high-density(0.35 μm period) recorded magnetic transitions;

DESCRIPTION OF THE PREFERRED EMBODIMENT

This invention relates generally to the field of scanning probemicroscopy and more particularly to a non-contact force microscopeutilizing a novel coaxially cantilevered microprobe tip configurationfor measuring a plurality of properties, including certain forces andforce gradients of a sample.

More particularly, the present invention pertains to a novel non-contactforce microscope identified by the general reference 10 as shown in FIG.1, and comprises a support structure 11, and a coaxial cantilever-tipconfiguration 12 shown in its installed position relative to supportstructure 11 in force microscope 10. A stage 14 is disposed in operativerelationship on support structure 11 beneath cantilever-tipconfiguration 12 to support sample 16. Piezo-electric-tube (PZT) drives18, 19, micrometer 20, rigid insulating disk 22, and collar 24 are alsoattached, directly or indirectly, to support structure 11 of forcemicroscope 10 as shown.

In a preferred embodiment of the present invention as shown in FIGS. 1and 2, a cantilever-tip configuration 12 is formed from a single nickelwire having an electrochemically etched sharpened tip portion 26 formedat one end thereof (tip portion 26 is shown, but need not necessarily becone-shaped). The remainder of the wire is shaped as an elongatedcantilever portion 27 with an unsharpened, blunt end portion (not shown)for insertion in collar Cantilever portion 27 has a longitudinallyextending axis which is in coaxial, operatively associated relationshipwith tip portion 26. Cantilever portion 27 is also chemically etched toreduce the cantilever stiffness. For scanning a sample 16, configurationis positioned in non-contact responsive relationship to sample as shownin FIG. 2. Tip portion 26 may also be formed of magnetized nickel whichallows the invention to operate as a magnetic force microscope tomeasure magnetic forces acting on tip portion 26 due to the interactionof the magnetic fields of sample 16 with tip portion

Force microscope 10 further comprises a capacitance probe 28 whichmeasures the differential capacitance relative to cantilever portion 27as configuration 12 oscillates over a sample 16. A second capacitanceprobe (not shown) can be added to measure a second differentialcapacitance relative to tip portion 26. Well known capacitance measuringand graphical imaging means (not shown) can be used to record anddisplay the capacitance data from either or both capacitance probes (ifused), in understood fashion. Technology exists which makes it possibleto electrically combine the data from both probes (if used), for displayon a single display device. Alternatively, a second, discrete measuringand imaging means may be used to simultaneously and independently recordthe data from a second capacitance probe (if such is used). Of course,the methods for capacitance retrieval, cumulation and display from theinputs are known or are simply obtainable by those skilled in the artand, without further description, such methods are thus incorporatedherein. Thus, multi-dimensional forces can be measured as describedbelow.

The key feature of the present invention is the simple, yet effective,coaxial structural orientation of cantilever-tip configuration 12. In apreferred embodiment, as shown in FIGS. 1 and 2, cantilever portion 27and tip portion 26 are formed from a single piece of wire. This processinvolves a sequence of electrochemical etching and mechanicalprocessing. Ferromagnetic nickel (Ni) is a preferred material of thewire for magnetic force microscopy, and a 70% nitric acid solution is asuitable etchant. Starting with a piece of wire approximately 1-mil(0,001"≈0.0025 cm) in diameter and 2 cm long, the finished shape ofconfiguration 12 is as shown with a sharpened tip portion 26 at the endof a cantilever portion 27 with an ultra-soft spring constant of ˜10⁻³N/m.

The formation process used in the preferred embodiment of cantilever-tipconfiguration 12 is substantially as follows. First, a sharpened tipportion 26 is formed at one end of a wire by applying a positive DCvoltage to the wire in an acid solution. The unsharpened, blunt endportion (not shown) of the wire is then inserted into a 0.1 mm I.D., 3mm long stainless steel collar 24. At this point, collar 24 is not yetattached to microscope 10. Rather, collar 24 facilitates handling thewire during processing and eventually serves to hold configuration 12 inrigid insulating disk 22 in support structure 11 of microscope 10.

Next, approximately 3 mm of the sharpened end of the wire (including tipportion 26) is pressed between two pieces of mirror-finish carbide in avise (not shown), to a thickness of about 5×10⁻⁵ cm. Cantilever portion27 is inserted through a 1 mm I.D., 1 mm long TEFLON® tube filled with70% nitric acid, leaving about 0.1 mm of sharpened tip portion 26protruding out of the etchant solution. During this final etchingprocess, a permanent magnet is placed close to the protruding tipportion 26, providing tension to help prevent delicate cantileverportion 27 from bending, and ensuring magnetic alignment along the axisof cantilever-tip configuration 12. After a specific interval of time(on the order of 30 seconds, depending on desired cantilever stiffness),configuration 12 is carefully removed and placed in an acetone bath toprevent further etching.

Finally, silver paint 30, which acts primarily as an adhesive or glue,is applied to collar 24, and cantilever-tip configuration 12 is pulledfurther into collar 24 until a ˜0.05 cm amount of configuration 12 isleft protruding out of collar 24. As paint 30 dries and thus rigidlysecures configuration 12 within collar 24, cantilever-tip configuration12 is carefully straightened by manipulating it with tweezers at thebase of cantilever portion 27. As shown in FIG. 2, typical finaldimensions of cantilever portion 27 are: length l≈0.05 cm, width w≈0.007cm, and thickness τ≈5×10⁻⁵ cm. Note, silver paint 30, as used in thepreferred embodiment, serves a secondary purpose of ensuring anelectrical connection between configuration 12 and collar 24. However,any epoxy or other adhesive could probably be used so long as thereremains a conductive electrical connection between configuration 12 andcollar 24.

To scan a sample 16, collar 24 with coaxial cantilever-tip configuration12 mounted therein, is mounted in insulating disk 22 in supportstructure 11 of microscope 10 in an orientation that is substantiallyperpendicular to the surface of sample 16, as shown in FIG. 2. Thepresent invention utilizes standard mechanisms for sample and tipmovement as described below. Sample 16 is mounted on stage 14 and israster scanned (rastered) under tip portion 26 in the X-Y plane by meansof a piezo-electric-tube (PZT) drive 18 which is shown as attached tomicroscope 1O in FIG. 1. A means of positioning sample 16 in propernon-contact responsive relationship to tip portion 26 includes adifferential micrometer 20 which is used for coarse vertical approach(along the Z-axis), with a single PZT drive 19 for fine verticaladjustments (both of which are also shown in FIG. 1).

Referring again to FIG. 2, further details of-the operation of coaxialcantilever-tip configuration 12 are shown. Deflections of configuration12 may be sensed using any of a plurality of standard techniques ormeans, such as the original Binnig tunneling current measurementassembly, or optical reflection measurement assembly, or opticalinterferometry measurement assembly (none of which are shown here), butfor reasons of compactness and versatility, the present embodiment usesa simple capacitive means, as described in Simpson et al., Rev. Sci.Instru., Vol. 48, page 1392 (1977), and incorporated herein by thisreference thereto. The capacitance between cantilever-tip configuration12, and capacitance probe 28 held near configuration 12, forms part ofan LC circuit coupled to an RF oscillator (not shown). Motion ofcantilever-tip configuration 12 with respect to stationary capacitanceprobe 28 changes the capacitance of the LC circuit, and thereby variesthe frequency of the oscillator, which is then detected and measured byan FM tuner (not shown ).

The mechanical resonance of the cantilever-tip configuration 12 may beexcited parametrically by oscillating vertical PZT 19 up-and-down attwice the resonance frequency of cantilever-tip configuration 12, orelectrostatically with an oscillating voltage across the gap betweenconfiguration 12 and capacitance probe 28 at one-half the mechanicalresonance frequency of cantilever-tip configuration 12. Resonance ismaintained using a common 2-phase lock-in amplifier and feedback circuit(not shown). Amplitude and frequency of oscillation of cantileverportion 27 are extracted directly from the lock-in amplifier, which arethen recorded and plotted as a function of the X- and Y-position ofsample 16. Again, well known graphical imaging means (also not shown)may be used to record and/or display the capacitance data in understoodfashion. As mentioned above, the measuring and display devices may beused separately or the data combined for display on a single device.These methods for capacitance retrieval, cumulation and display whetherfrom singular or dual inputs are well known or are simply achievable andneed not be described further herein.

Referring now to FIGS. 3(a)-3(c), a profile of the magnetic forcesbetween tip portion 26 and a sample 16 under study may be generated bymeasuring changes in the mechanical resonance frequency of theoscillating coaxial cantilever-tip configuration 12 while rasteringsample 16 on stage 14. FIG. 3(b) shows that measured variations in theresonance frequency as a function of position along a single line of theimage in FIG. 3(a). FIG. 3(c) shows expected or calculated variations inthe resonance frequency as a function of position along a single line ofthe image in FIG. 3(a), according to the calculations set forth below.

Motion of cantilever-tip configuration 12 is detected by variations inthe capacitance between cantilever portion 27 and capacitance probe 28.Changes in the mechanical resonance frequency and position ofcantilever-tip configuration 12 are detected as a function of sample 16position. These changes correspond to the forces and force gradients ofsample 16 acting on configuration 12. Again, a second capacitance probe(not shown) could be introduced to simultaneously measure the motion ofcantilever-tip configuration 12, and hence the forces and forcegradients from the sample in an independent direction. Thus, in thisalternative embodiment, two capacitance probes may be positioned atninety degrees relative to each other, and cooperate to measuredeflections representing multiple independent components of sampleforces acting on configuration 12.

The present invention is especially effective when operated as anon-contact force microscope 10, with tip portion 26 held at distancesof 1-100 nm from sample 16. If tip portion 26 is made from a magnetizedmaterial, the invention allows measurements of magnetic forces acting ontip portion 26 resulting from the interaction between tip portion 26 andthe magnetic fields of sample 16.

In the preferred embodiment of the present invention, an ultra-smallcantilever spring constant is vital for maximum force sensitivity. Thespring constant for a rectangular cantilever portion 27 may becalculated from k=Eτ³ w/41³. (See: Shock and Vibration Handbook 2^(nd)edition, pgs. 7-11 to 7-16, edited by C. M. Harris and C. E. Crede,McGraw-Hill, New York (1976)). Using a typical width (w=0.006 cm),thickness (τ=3×10⁻⁵ cm), and length (l=0.05 cm) of a cantilever portion27 of the present embodiment of the invention, and the elastic modulusof nickel E=2.07×10¹² dyne/cm², a characteristic spring constant iscalculated to be:

    k≈1 dyne/cm=1×10.sup.-3 N/m.

This is an order of magnitude smaller than previously reported "soft"cantilever force microscopes, and nine orders of magnitude less than thequartz crystal cantilever system of Pohl.

An experimental value for the effective spring constant may bedetermined from the mechanical resonance frequency of cantilevertipconfiguration 12. Assuming a uniform cantilever portion 27, withmass-per-unit-length λ=wτρ (where the mass density is ρ=8.9 g/cm³ fornickel), an unperturbed cantilever-tip configuration 12 of length l hasa resonance frequency of f₀ =[0.16152(τ)/l² ](E/ρ)^(1/2). (See: Shockand Vibration Handbook 2^(nd) edition, pgs. 7-11 to 7-16, edited by C.M. Harris and C. E. Crede, McGraw-Hill, New York (1976).) Thus,replacing the cantilever thickness (which is usually the most difficultparameter to measure accurately) by τ=(f₀ l² /0.16152)(ρ/E)^(1/2), thespring constant of cantilever-tip configuration 12 (k=Eτ³ w/4l³) may bewritten k=(f₀ l)³ wρ(ρ/E)^(1/2) /0.01686. Using measured values for thelength (l=0.05 cm), width (w=0.006 cm) and resonant frequency (1,100 Hz)of a particular cantilever portion 27, with the known mass density(ρ=8.9 g/cm³) and elastic modulus (E=2.07×10¹² dyne/cm²) of nickel, anexperimental value for the effective spring constant is

    k≈1 dyne/cm=10.sup.-3 N/m,

which agrees with the theoretically determined value given above.

Perhaps the most relevant technique for calibrating the sensitivity ofcoaxial cantilever-tip configuration 12 is to measure the frequencychange from a known applied force, which can then be compared to theexpected frequency change for an idealized cantilever portion 27.Expected frequency changes may be calculated by analyzing all of theforces acting on cantilever portion 27 and tip portion 26, but it isperhaps simpler to use an energy analysis. For simple linear (elastic)forces that obey Hooke's law (generally valid for small displacements),the virial theorem states that the time-averaged kinetic energy equalsthe time-averaged potential energy: <T>=<V>. Furthermore, for suchlinear forces, the average of the sum of internal elastic energy plusexternal potential energy is equal to the sum of the average: <V>=<V₀+V_(E) >=<V₀ >+<V_(E) >. Thus, if the oscillation amplitude is heldconstant so that the average internal elastic energy of cantilever-tipconfiguration 12 is constant, then variations in the mechanicalresonance frequency (which change the average kinetic energy) are dueprimarily to changes in the interaction potential energy δ<T>=δ<V_(E) >.

Assuming that the time-dependent displacement at tip portion 26 isδX_(t) =Acos(2πf₀ t), where A is an amplitude of oscillation, thelateral motion at a distance Z from the cantilevered end is: ##EQU1##where Z₀ =l/1.875. Using <sin² (2πf₀ t)>=<cos² (2πf₀ t)>=1/2, the timeaverage kinetic energy is found by integrating 1/2λx² over the length ofcantilever portion 27 <T>=0.0625λl(2πfA)², and the expected resonantfrequency becomes f² =f₀ ² +4<V_(E) >/(λlπ² A²). For small externalforces, the change in the resonant frequency is Δf=f-f₀ ≈2<V_(E) >/(f₀λlπ² A²). To lowest order, only potential energy terms which arequadratic in tip displacement contribute to a frequency shift, i.e.terms for which V_(E) ∝(δX)². Contributions to <V_(E) > come from forcesalong the axis of cantilever portion 27, and force gradients in thedirection of cantilever oscillation. In contrast to prior arthorizontally disposed cantilever-tip configurations, whose mechanicalresonance frequency is sensitive primarily to vertical force gradients,the present invention, with a vertically disposed coaxialcantilevered-tip configuration 12, is sensitive to vertical forces andhorizontal force gradients.

As an example, consider the frequency shift due to gravity. For ahorizontal cantilever (not shown), the average potential energy fromtime spent above equilibrium is equal and opposite to that from timespent below equilibrium, hence <V_(E) >=0; the resonance frequency of ahorizontal cantilever is not sensitive to gravity since thegravitational force has negligible gradient. This behavior is verifiedby orienting the invention so that the cantilever is horizontal. Towithin experimental resolution, the cantilever resonance frequency doesnot depend on the angle of rotation about the horizontal axis.

For a vertically hanging cantilever portion 27 (anchored at its top, asdescribed herein), the minimum in V_(E) occurs at equilibrium, whencantilever portion 27 hangs straight down. When oscillated aboutequilibrium, an element of mass at Z rises a distance δZ=∫₀ ^(z) dl-Zwhere the cantilever element of length is dl=√{1+[d(δX)/dZ]² }dZ. Forsmall oscillations dl≈{1+1/2[d(δX)/dZ]² }dZ gives <V_(E) >=λg<∫₀ ^(l)(δZ)dZ>=λgπA² /32, or Δf≈g/(16πlf₀). For a typical cantilever portion 27of length l=0.05 cm, which had a resonance frequency of f₀ =1,100 Hz,the calculated frequency change when the cantilever is rotated to liehorizontally is Δf=0.35 Hz, in good agreement with the measured decreaseof Δf=0.38±0.05 Hz. In principle, the elastic forces of a verticallyhanging cantilever portion 27 may be reduced further until gravityprovides the dominant restoring force, but noise and scan-rateconsiderations limit the practicality of such low-frequencyoscillations. The fact that one can readily measure changes in themechanical resonance frequency due to gravity verifies that cantileverportion 27 is nearing the theoretical limit for minimal restoring force.It is problematic to use such soft cantilevers, which sag under theirown weight, in a microscope with a cantilever that is orientedsubstantially parallel to the sample's surface, as in the originalBinnig AFM.

The coaxially cantilever-tip configuration 12 is exceptionally sensitiveto force interactions between tip portion 26 and sample 16, thus it isideally suited for measuring long-ranged forces at non-contactdistances. One example, as described below, is the microscopic magneticforces between a magnetized sample 16 and a magnetized tip portion

The magnetostatic potential of a point dipole in a magnetic field isV_(E) =-m.sup.. H. For a dipole of magnitude m₀ aligned upward along theaxis of tip portion 26 m=m₀ (-sinθ,0, cosθ). For small displacementsfrom equilibrium (δX and δZ), the angle tip portion 26 makes withrespect to the (vertical) Z -axis is θ≈dX/dZ=1.3764δX/l. Significantterms in a Taylor-series expansion of the magnetic field are H≈H₀+(∂H/∂X)δX_(t) +(∂H/∂Z) δZ_(t) +1/2(∂² H/∂X²) (δX_(t))². At tip portion26, the X-displacement (δX_(t)) ranges between -A and +A, whereas theZ-displacement is δZ_(t) =1/2∫₀ ^(ll/Zo) (dX/dZ)² dz=0.58088 (δX)² /l.Quadratic terms in the potential which survive time-averaging are##EQU2## which then leaves ##EQU3## Magnetic structures of size γgenerally have stray fields which vary over length scales of order γ, sothat γ² (∂² H_(z) /∂z²)˜γ(∂H_(z) /∂z)˜H₀ z. Thus, microscopic magneticstructures with γ<<l have l² ∂² H_(z) ∂x² >>l∂H_(z) /∂z>>H_(0z), and thedominant term which contributes to observed frequency change is Δf≈m₀(∂² H_(z) /∂x²)/(2f₀ λπ² l).

The magnetic microstructure of the longitudinally polarized video signalon pre-recorded VHS magnetic tape was measured. The magnetic tape iscomprised of a layer of Fe₂ O₃ /Co compound on a mylar substrate. Forcemicroscopy of this tape reveals a uniformly rough surface with no largescale features. When viewed with the MFM of the present invention, asshown in FIG. 3(a), the magnetic bit structure is clearly visible. Tomodel this image, we first consider a single arctangent magnetictransition (reorientation of the magnetization) from -M_(r) x to M_(r)x, over the transition width (a) centered about x=0, recorded to a depth(δ) in the magnetic media. Assuming that the bits are much longer(Y-axis) than they are wide (X-axis), the demagnetization field andderivatives of interest are: ##EQU4## See: R. I. Potter, J. Appl. Phys.41, 1648 (1970) and D. Rugar, H. J. Mamin, P. Guenther, S. E. Lambert,J. E. Stern, I. McFadyen, and T. Yogi, J. Appl. Phys. 68, 1169 (1990).

For a vertically cantilevered tip portion 26, the dominant contributionto magnetic contrast for small magnetic structures comes from theintegral of a ∂² H_(z) /∂x² over the volume of tip portion 26. Assuminga tip portion 26 of macroscopic height, with a cross-section that neverdecreases with increasing height, the volume integral may be convertedto an integral over the surface of tip portion 26 using ∂² H_(z) /∂x² =-7 ² H_(z) /∂z² : ##EQU5##

For a cone-shaped tip portion 26, this surface integral contains termswhich do not depend on lateral position, including a term which divergeslogarithmically with the height of the cone. These terms, however, donot contribute to the lateral resolution and hence may be ignored as aconstant background frequency shift. For a cone of half-angle α,centered a distance x₀ from the transition at a height z₀ above themagnetic media, the spatially dependent components which contribute tocontrast are: ##EQU6##

The term in I(x₀,z₀) which diverges logarithmically with x₀ ²δ may beremoved by considering multiple transitions with alternatingorientation. For the frequency modulated luminescence signal in VHSrecording technology, bits have alternating orientation with widthsW=0.5-0.8 μm. Assuming constant bit width, the net frequency shiftbecomes: ##EQU7##

Using appropriate values for the length l=0.05 cm, conic angle 2α=10°,unperturbed resonance frequency f₀ =1 kHz, scan height z₀ =500 nm, andmagnetization density m₀ =500 emu/cm³ of nickel; as well as reasonablevalues for recording depth δ=50 nm, transition width a=300 nm, bit widthW=0.83 μm, and media magnetization Mr=500 emu/cm³, qualitative andquantitative agreement between observed (FIG. 3(b)) and calculated (FIG.3(c)) magnetic contrast are obtained.

Referring to FIGS. 4(a)-4(b), the intrinsic capabilities for coaxialcantilever-tip configuration 12 to resolve directional information aredemonstrated. In essence, a single magnetic transition is a line wheretwo rows of oppositely oriented magnetic dipoles meet. For example, onerow has all their poles pointing in one direction [e.g. north (N) in the+x direction], while the other row has its poles oriented in theopposite direction (N in the -x direction), so that the transition is aline between two rows of N poles. An opposite transition occurs alongthe line between two south (S) poles. Considerable magnetic flux isexpelled out of the recording media along the line where the N polesmeet, and this magnetic flux is returned back into the media along theline where the S poles meet. In VHS technology, changes in the distancebetween these transitions are converted into a frequency modulatedsignal that contains the recorded video image. FIG. 4(a) is an image ofVHS recorded tape taken with tip portion 26 oscillating in theX-direction (perpendicular to the transition lines) demonstrating alarge contrast due to the large changes in the magnetic force as themagnetic field makes transitions from the +x direction to the -xdirection. FIG. 4(b) is an image of a similarly recorded region of theVHS tape, but with tip portion 26 oscillating in the Y-direction(parallel to the transition lines) revealing only small changes in themagnetic fields along the transitions. The contrast between FIGS. 4(a)and 4(b) demonstrate the high sensitivity of coaxial cantilever-tipconfiguration 12 for resolving directional information.

The mechanism for directional contrast demonstrated in FIGS. 4(a)-(b) isintrinsic, hence it does not require a special orientation of themagnetized tip. Similar contrast between force-gradients in the X- andY-directions may be obtained when operated as a general purposenon-contact force microscope be. The original Binnig configuration, withthe cantilever oriented parallel to the sample's surface, cannot resolvedifferences in the X- and Y- force gradients since the tip can only bevibrated in the Z-direction (normal to the sample). A further intrinsicadvantage of coaxial cantilever-tip configuration 12 is that, if asecond capacitance probe (or other independent vibration detectionsystem) were installed, it would be possible to measure motion ofcantilever portion 27 simultaneously in the X- and Y-directions,allowing concurrent detection of both lateral components of the forcegradient.

Referring to FIG. 5, yet another intrinsic advantage of coaxialcantilever-tip configuration 12 can be seen. In s-VHS technology thedensity of recorded information is increased by superimposing ahigh-fidelity sound signal onto a standard VHS video signal. The soundsignal is recorded at a lower frequency, so that it is embedded deeperinto the magnetic recording media, essentially utilizing all threedimensions of the media. The resulting recorded structure is quitecomplex, making it difficult to resolve using previous techniques formagnetic microscopy. Since coaxial cantilever-tip configuration 12 isvibrated laterally over the sample's surface, it is ideally suited forresolving changes in the magnetic field as a function of lateralposition over the magnetic recording media, which is most closelyrelated to the signal that is sensed by a magnetic read head. In FIG. 5it is shown that, even when scanned over a large scale, a microscope 10employing the present invention is able to clearly resolve all of thecomplex structures of the s-VHS recording.

Magnetic microstructures small enough to clearly establish the ultimateresolution of force microscope 10 of the present invention have not yetbeen examined. Nevertheless, close examination of magnetic force imagesfrom the VHS recording tape (FIG. 6), reveals structure indicative ofthe individual magnetic particles which comprise the magnetic recordingmedia. This shows that the resolution of the present inventionsignificantly exceeds the typical particle diameter of ˜100 nm; thissimple tabletop force microscope 1O, used as an MFM, provides unexpectedresolution on the order of 10 nm, comparable to highly sophisticated,state-of-the-art magnetic force microscopes.

From the foregoing, it is readily apparent that a useful embodiment ofthe present invention has been herein described and illustrated whichfulfills all of the aforestated objectives in a remarkably unexpectedfashion. It is, of course, understood that such modifications,alterations and adaptations as may readily occur to the artisanconfronted with this disclosure are intended within the spirit of thisdisclosure which is limited only by the scope of the claims appendedhereto.

Accordingly we claim:
 1. A cantilever-tip configuration for use in anon-contact force microscope for measuring selected forces and forcegradients of a sample, said configuration comprising an elongatedcantilever portion and a sharpened tip portion operatively associatedwith and disposed in substantially coaxial relationship with saidcantilever portion.
 2. A cantilever-tip configuration according to claim1 in which said cantilever portion and said tip portion are formed froma single piece of wire, said tip portion being disposed at one end ofsaid wire, and having means for operatively installing saidconfiguration in a non-contact force microscope.
 3. A cantilever-tipconfiguration according to claim 1 in which the geometry of saidconfiguration inhibits axial deflections toward said sample.
 4. Acantilever-tip configuration according to claim 3 in which saidcantilever portion has a low static spring constant.
 5. A cantilever-tipconfiguration according to claim 1 further comprising means formeasuring deflections of said configuration in response to selectedforces and force gradients of said sample.
 6. A cantilever-tipconfiguration according to claim 5 in which said means for measuringdeflections of said configuration comprises a capacitance measurementassembly.
 7. A cantilever-tip configuration according to claim 2 inwhich said wire is nickel.